Clumpiness of Dark Matter and Positron Annihilation Signal: Computing the odds of the Galactic Lottery

TL;DR

This paper investigates how the uncertain, clumpy distribution of dark matter in the Milky Way affects the predicted positron annihilation signals, highlighting the energy dependence and variability of the boost factor.

Contribution

It provides a statistical framework combining analytical and numerical methods to estimate the uncertainty in dark matter annihilation signals due to clumpiness.

Findings

The boost factor varies with energy and particle type.

Clumpiness introduces significant uncertainty in positron signals.

Results are applied to interpret HEAT positron measurements.

Abstract

The small-scale distribution of dark matter in Galactic halos is poorly known. Several studies suggest that it could be very clumpy, which turns out to be of paramount importance when investigating the annihilation signal from exotic particles (e.g. supersymmetric or Kaluza-Klein). In this paper we focus on the annihilation signal in positrons. We estimate the associated uncertainty, due to the fact that we do not know exactly how the clumps are distributed in the Galactic halo. To this aim, we perform a statistical study based on analytical computations, as well as numerical simulations. In particular, we study the average and variance of the annihilation signal over many Galactic halos having the same statistical properties. We find that the so-called boost factor used by many authors should be handled with care, as i) it depends on energy and ii) it may be different for positrons, antiprotons and gamma rays, a fact which has not received any attention before. As an illustration, we use our results to discuss the positron spectrum measurements by the HEAT experiment.